\select@language {spanish}
\select@language {spanish}
\contentsline {chapter}{Prefacio}{7}{chapter*.3}
\contentsline {chapter}{Introducci\'on}{11}{chapter*.4}
\contentsline {chapter}{\numberline {1}$P$-c\IeC {\'\i }rculos y el diagrama de Voronoi del punto m\IeC {\'a}s lejano}{17}{chapter.1}
\contentsline {section}{\numberline {1.1}Nuestro problema}{17}{section.1.1}
\contentsline {section}{\numberline {1.2}El diagrama de Voronoi del punto m\IeC {\'a}s \\ lejano}{18}{section.1.2}
\contentsline {subsection}{\numberline {1.2.1}\IeC {\textquestiondown }Qu\IeC {\'e} es el Diagrama de Voronoi del punto m\IeC {\'a}s lejano?}{19}{subsection.1.2.1}
\contentsline {subsection}{\numberline {1.2.2}Calculando el diagrama de Voronoi}{24}{subsection.1.2.2}
\contentsline {section}{\numberline {1.3}$P$-c\IeC {\'\i }rculos de radio m\IeC {\'\i }nimo}{26}{section.1.3}
\contentsline {subsection}{\numberline {1.3.1}Calculando el $P$-c\IeC {\'\i }rculo de radio m\IeC {\'\i }nimo}{29}{subsection.1.3.1}
\contentsline {chapter}{\numberline {2}$P$-c\IeC {\'\i }rculo de radio m\IeC {\'\i }nimo con centro en una l\IeC {\'\i }nea de consulta}{31}{chapter.2}
\contentsline {section}{\numberline {2.1}Nuestro problema}{31}{section.2.1}
\contentsline {section}{\numberline {2.2}El $P$-c\IeC {\'\i }rculo de radio m\IeC {\'\i }nimo con centro en $L$}{32}{section.2.2}
\contentsline {subsection}{\numberline {2.2.1}Calculando el $P$-c\IeC {\'\i }rculo de radio m\IeC {\'\i }nimo con centro sobre una l\IeC {\'\i }nea recta}{35}{subsection.2.2.1}
\contentsline {section}{\numberline {2.3}Encontrando a $C_L$ mediante consultas din\IeC {\'a}micas}{38}{section.2.3}
\contentsline {subsection}{\numberline {2.3.1}Esquema del algoritmo}{38}{subsection.2.3.1}
\contentsline {subsection}{\numberline {2.3.2}$c_L$ y las trayectorias sobre el \IeC {\'a}rbol $\mathcal {V}(P)$}{40}{subsection.2.3.2}
\contentsline {subsection}{\numberline {2.3.3}Estructura de datos sobre $\mathcal {V}(P)$}{44}{subsection.2.3.3}
\contentsline {subsection}{\numberline {2.3.4}El algoritmo}{45}{subsection.2.3.4}
\contentsline {chapter}{\numberline {3}Separabilidad por c\IeC {\'\i }rculos entre pol\IeC {\'\i }gonos convexos}{47}{chapter.3}
\contentsline {section}{\numberline {3.1}Nuestro problema}{47}{section.3.1}
\contentsline {section}{\numberline {3.2}C\IeC {\'\i }rculos separadores}{49}{section.3.2}
\contentsline {section}{\numberline {3.3}El algoritmo}{53}{section.3.3}
\contentsline {subsection}{\numberline {3.3.1}Precisando la posici\IeC {\'o}n de $c$}{56}{subsection.3.3.1}
\contentsline {subsection}{\numberline {3.3.2}Algoritmo para encontrar $q_{c}$}{58}{subsection.3.3.2}
